multichoose

multiset combinations of k out of n (n multichoose k)

Overview

This library implements an efficient loopless multiset combination generation algorithm which is (approximately) described in "Loopless algorithms for generating permutations, combinations, and other combinatorial configurations." G Ehrlich - Journal of the ACM (JACM), 1973. (Algorithm 7.)

The method generates all multisets that would be generated from taking k elements from a multiset of n. Repeated multisets are possible if the input set contains repeated elements. The number of multiset combinations equals the multinomial coefficient (n multichoose k).

Usage

node.js implementation

Install via

npm install -g multichoose

var multichoose = require('multichoose')
multichoose(2, [1,2,3], console.log)
// [ 1, 1 ]
// [ 1, 2 ]
// [ 1, 3 ]
// [ 2, 2 ]
// [ 2, 3 ]
// [ 3, 3 ]

% multichoose 3 A B C
A A A
A A B
A A C
A B B
A B C
A C C
B B B
B B C
B C C
C C C

multichoose.cpp

Include is a C++ library/program which contains a generic function to generate multisets for vectors of any type of object. You can test out the program using strings input from the command line by typing:

% make

Running the bare executable prints usage information:

% ./multichoose
usage: 
./multichoose <k> <item1> <item2> ... <itemN>  ~ n multichoose k

Example usage:

% ./multichoose 2 a t g c
a a 
a t 
a g 
a c 
t t
t g 
t c 
g g 
g c 
c c

This example lists all the possible unordered genotypes at a given genetic loci of which there are two copies (e.g. chromosomes). In this case k (=2) could be understood as the expected ploidy of the given locus.

(Note that this is not currently built as the default binary for the npm module, which uses cli.js.)

multichoose.py

A python library implementation is also included for those who like to indent their code consistently.

multiset permutations

TODO: These will be factored into a separate module.